Question
A train can cross a pole in 18 seconds. When the length of
the train is increased by 50 metres, it now takes 169 seconds to overtake a car running in the same direction at 14 m/s. Find the original length of the train.Solution
Let the original length and speed of the train be 'l' metres and 's' m/s respectively.
(l / s) = 18
⇒ l = 18s ...(i)
According to the question,
[(l + 50) / (s - 14)] = 169
⇒ 18s + 50 = 169(s - 14)
⇒ 18s + 50 = 169s - 2366
⇒ 151s = 2316
⇒ s = 16
Therefore, l = 18 × 16 = 288 metres
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